The Gleason property for Reinhardt domains
type: Item
instance of: scholarly article
title: The Gleason property for Reinhardt domains
zbMATH Open document ID: 0869.32001
author: U. Backlund
author: A. Fällström
published in: Mathematische Annalen
publication date: 1997-09-11T00:00:00Z
review text: We prove that bounded pseudoconvex Reinhardt domains in \(\mathbb{C}^2\) with \(C^2\)-boundary have the Gleason \(A\)-property. The main difficulties occur when the base point \(p\) is close to the boundary, but at the same time far away, in a sense, from the set of strictly pseudoconvex points. As a first auxiliary result we solve a \(\overline\partial\)-equation in pseudoconvex Reinhardt domains in \(\mathbb{C}^2\) with \(C^2\)-boundary. The crucial step in the proof of the main theorem is a lemma which says that one can always find analytic polynomials with certain properties that enable us to construct a finite open covering of the closure of the domain. The covering is constructed so that the pairwise intersections of its open sets intersect the boundary of the domain only in strictly pseudoconvex points and is in turn used to formulate an additive Cousin problem. We solve this problem using the above-mentioned \(\overline \partial\)-result.
Mathematics Subject Classification ID: 32A07
Mathematics Subject Classification ID: 46J15
Mathematics Subject Classification ID: 32W05
zbMATH DE Number: 1031501
zbMATH Keywords: Gleason \(A\)-property
zbMATH Keywords: \(\overline\partial\)-equation
zbMATH Keywords: Reinhardt domains
MaRDI profile type: Publication
full work available at URL: s002080050066
OpenAlex ID: W2018422286
DOI: 10.1007/S002080050066
description: scientific article; zbMATH DE number 1031501